In "continuous" mathematics there are several important notions such as covering space, fibre bundle, Morse theory, simplicial complex, differential equation, real numbers, real projective plane, etc. that have a "discrete" analog: covering graph, graph bundle, discrete Morse theory, abstract simplicial complex, difference equation, finite field, finite projective plane, etc. I would like to know if there are others. But the real question is:
Are there any important "continuous" mathematical concepts without "discrete" analog and vice versa?
[Math] Are there any important mathematical concepts without discrete analog
co.combinatoricsmetamathematicssoft-question
Best Answer
A lot of ideas from topology and analysis don't have obvious discrete analogues to me. At least, the obvious discrete analogues are vacuous.
The interior of a set.I think a better question is which ideas have surprisingly interesting discrete analogues, like cohomology or scissors congruence.